The Nuclear Incompressibility parameter is one of three important components characterizing the nuclear equation of state. It has crucial bearing on diverse nuclear and astrophysical phenomena, including radii of neutron stars, strength of supernova collapse, emission of neutrinos in supernova explosions, and collective flow in medium- and high-energy nuclear collisions. The only direct experimental measurement of this parameter comes from the compressional-mode giant resonances—the isoscalar giant monopole resonance (ISGMR) or the “breathing mode”, and the isoscalar giant dipole resonance (ISGDR) or the “squeezing mode”. In this talk I will review current status of the research on direct experimental determination of nuclear incompressibility. In particular, recent measurements on a series of Sn and Cd isotopes have provided an "experimental" value for the asymmetry term of nuclear incompressibility which is critical to our understanding of neutron stars.